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Hypothesis Testing - Chi Squared Test
Usually, the null hypothesis is boring and the alternative hypothesis is interesting. For example, let's say you feed chocolate to a bunch of chickens, then look at the sex ratio in their offspring. If you get more females than males, it would be a tremendously exciting discovery: it would be a fundamental discovery about the mechanism of sex determination, female chickens are more valuable than male chickens in egg-laying breeds, and you'd be able to publish your result in Science or Nature. Lots of people have spent a lot of time and money trying to change the sex ratio in chickens, and if you're successful, you'll be rich and famous. But if the chocolate doesn't change the sex ratio, it would be an extremely boring result, and you'd have a hard time getting it published in the Eastern Delaware Journal of Chickenology. It's therefore tempting to look for patterns in your data that support the exciting alternative hypothesis. For example, you might look at 48 offspring of chocolate-fed chickens and see 31 females and only 17 males. This looks promising, but before you get all happy and start buying formal wear for the Nobel Prize ceremony, you need to ask "What's the probability of getting a deviation from the null expectation that large, just by chance, if the boring null hypothesis is really true?" Only when that probability is low can you reject the null hypothesis. The goal of statistical hypothesis testing is to estimate the probability of getting your observed results under the null hypothesis.
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If the expected number of observations in any category is too small, the chi-square test may give inaccurate results, and you should use an instead. See the for discussion of what "small" means.
X-squared = 14.8292, p-value = 0.01177
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So which test is better when we have a 2 × 2 table? The are the same from statistical decision standpoint: A signficant Chi-square test would be similar to concluding a difference in the two proportions. The benefit of the two-proportion test is that we can calculate a confidence interval for this difference to generate an estimate of just how large the difference might be.
When we run a Chi-square test of independence on a 2 × 2 table, the resulting Ch-square test statistic would be equal to the square of the Z-test statistic from the Z-test of two independent proportions. Consider the following example where we form a 2 × 2 for the Political Party and Opinion by only considering the Favor and Opposed responses:
You would report this as "chi-square=0.3453, 1 d.f., P=0.5568."
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The technique to analyze a discrete outcome uses what is called a chi-square test. Specifically, the test statistic follows a chi-square probability distribution. We will consider chi-square tests here with one, two and more than two independent comparison groups.
The greater thecalculated chi-square value, the more likely the sample does notconform to the expected frequencies, and therefore you would reject thenull hypothesis.
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(We were given the chi-squared value)
A related criticism is that a significant rejection of a null hypothesis might not be biologically meaningful, if the difference is too small to matter. For example, in the chicken-sex experiment, having a treatment that produced 49.9% male chicks might be significantly different from 50%, but it wouldn't be enough to make farmers want to buy your treatment. These critics say you should estimate the effect size and put a on it, not estimate a P value. So the goal of your chicken-sex experiment should not be to say "Chocolate gives a proportion of males that is significantly less than 50% (P=0.015)" but to say "Chocolate produced 36.1% males with a 95% confidence interval of 25.9 to 47.4%." For the chicken-feet experiment, you would say something like "The difference between males and females in mean foot size is 2.45 mm, with a confidence interval on the difference of ±1.98 mm."
Hypothesis Testing - Chi Squared Test - Boston …
When I ran a t test it looks like I can reject the null. How can I determine which to use, t or F testing?
t-Test: Two-Sample Assuming Unequal Variances
for the chi-square distribution with ..
This criticism only applies to two-tailed tests, where the null hypothesis is "Things are exactly the same" and the alternative is "Things are different." Presumably these critics think it would be okay to do a one-tailed test with a null hypothesis like "Foot length of male chickens is the same as, or less than, that of females," because the null hypothesis that male chickens have smaller feet than females could be true. So if you're worried about this issue, you could think of a two-tailed test, where the null hypothesis is that things are the same, as shorthand for doing two one-tailed tests. A significant rejection of the null hypothesis in a two-tailed test would then be the equivalent of rejecting one of the two one-tailed null hypotheses.
divides the chi-square distribution into a Fail to ..
I’m currently undertaking a forecast comparison on two aircraft manufacturers and would like to know what tests would be ideal to use if i wish to compare the two together? Chi square, T test or paired T test? Look forward to hearing from you.
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